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Yes there are problems related to tail docking dogs, as is shown in the docking wiki.

When I studied animal husbandry and anatomy of the dog, whilst studying Veterinary Science, we were taught the following.

Health

Depending on where the tail is docked, usually the tail is docked reasonably close to the body. Part of the dog's sphincter muscles that are used to assist in defecation are located at the base of the tail. Tail docking can sever these muscles.

Severing these muscles has been found to lead to fecal incontinence in some dogs. It can also make relieving blocked anal glands more difficult, as it is harder to pull the stub of the tail up when trying to express the glands.

Behavior

On a socialization front, tail docking removes part of a dog's key means of communication. More dominant or aggressive dogs will have upright tails, a submissive or frightened dog will have a lower tail or tail between the legs. For more aggressive breeds, such as dobermans and rottweilers, there has been a problem with other dog's perceiving them to be friendlier than they actually are, as the absence of a tail, can make the dog appear to be less dominant. Such a dog would, usually approach other dogs with an erect tail.

This misinterpretation of body language can land some dog's into trouble and an increased likelihood of dog fights with dominant or aggressive dog's that have docked tails.

You can read more about these risks and other problems at the AMVA website.

In many countries cosmetic tail docking is considered inhumane and is illegal.